1. Field of the Invention
The present invention relates to a matrix generation apparatus, method, and program for generating a transformation matrix for performing projection from input data to output data, and an information processing apparatus.
2. Description of the Related Art
Super resolution technology for transforming a low resolution image into a high resolution image using a transformation matrix obtained by principal component analysis (PCA), singular value decomposition (SVD), or high order singular value decomposition (HOSVD) is known as described, for example, in Japanese Unexamined Patent Publication No. 2008-192031, U.S. Pat. No. 7,693,351, Japanese Unexamined Patent Publication No. 2004-213108, and U.S. Pat. No. 7,133,048. This is a technology that, when an unknown low resolution image is inputted, transforms the low resolution image into a high resolution image using a transformation matrix obtained with respect to each object by principal component analysis (PCA) or high order singular value decomposition (HOSVD) using sample data.
One method for obtaining a transformation matrix through the high order singular value decomposition (HOSVD) is described in K. Jia and S. Gong, “Generalized Face Super-Resolution”, IEEE Trans Image Process, Vol. 17, No. 6, pp. 873-886, 2008 (Hereinafter, “Non-Patent Document 1). In the Non-Patent Document 1, a pair of sample images of low resolution information and a high resolution image is provided as images used for learning and a transformation matrix is learned through high order singular value decomposition (HOSVD) in advance using the transformation relationship of the pair sample images. Here, a tensor representing a transformation relationship in each modality feature space is calculated, such as a case in which a low resolution pixel is projected into an individual difference feature space after being projected into a feature space, and further from the individual difference feature space to a high resolution pixel. Then the number of modality variations (face orientations, illumination variations, races, and the like) for transformation can be represented by the rank of the tensor (i.e., a learning model can be designed), and a high accurate restoration can be achieved by performing transformation with an input condition being satisfied.
In order to obtain a transformation matrix (U·Σ·V) for generating a high resolution image from a low resolution image, as in Non-Patent Document 1, it is necessary to obtain U and V first and then Σ. Thus, it is inevitably required to calculate base U and base V, thereby causing a problem that the calculation time for the transformation matrix can not be reduced.
In view of the circumstances described above, it is an object of the present invention to provide a matrix generation apparatus, method, and information processing apparatus capable of efficiently generating a transformation matrix having high transformation accuracy. It is a further object of the present invention to provide a computer readable recording medium on which is recorded a matrix generation program for causing a computer to perform the matrix generation method described above.